# Haagerup's phase transition at polydisc slicing

@inproceedings{Chasapis2022HaagerupsPT, title={Haagerup's phase transition at polydisc slicing}, author={Giorgos Chasapis and Salil Singh and Tomasz Tkocz}, year={2022} }

. We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pe lczy´nski polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p -norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions.

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